Efficient low-temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence numerically exact results. To represent effects the bath, reservoir correlation functions are usually decomposed into summation multiple exponential terms in HEOM method. Since become highly non-Markovian at low temperatures or when bath has complex band structures, a present challenge obtain decompositions that allow efficient simulation with HEOM. In this work, we employ barycentric representation approximate Fermi function and hybridization frequency domain. This method, by approximating these optimized rational decomposition, greatly reduces number basis decomposing functions, further be applied ultralow temperature general structures. We demonstrate efficiency, accuracy, long-time stability decomposition scheme applying it Anderson impurity model low-temperature regime Lorentzian tight-binding functions.